Systems for comparing electrical signals

ABSTRACT

The present invention features a system for comparing the amplitudes and signs of two simultaneous electrical signals. A chain of discriminators is arranged to determine with successively greater resolution the angle P tan -1 X/Y) where X and Y respectively have the signs and amplitudes of each of the said two signals. In each discriminator except the first in the chain means are provided for inhibiting or correcting errors in the immediately preceding discriminator.

United States Patent Inventor Ralph Levy Leeds, England Appl. No.853,002

Filed Aug. 28, 1969 Patented Dec. 28, 1971 Assignee U.S. PhilipsCorporation New York, N.Y.

Continuation of application Ser. No. 487,765, Sept. 16, 1965, nowabandoned. This application Aug. 28, 1969, Ser. No. 853,002

SYSTEMS FOR COMPARING ELECTRICAL SIGNALS 4 Claims, 13 Drawing Figs.

U.S. Cl 340/347 AD, 343/124, 328/146, 340/178, 324/85 Int. Cl 03k 13/02Field of Search 340/347,

[5 6] References Cited UNITED STATES PATENTS 3,068,456 12/1962 Nevius340/347 X Primary Examiner-Maynard R. Wilbur Assistant Examiner-CharlesD. Miller Attorney- Frank Trifari ABSTRACT: The present inventionfeatures a system for comparing the amplitudes and signs of twosimultaneous electrical signals. A chain of discriminators is arrangedto determine with successively greater resolution the angle tan 1 X/Y)where X and Y respectively have the signs and amplitudes of each of thesaid two signals. In each discriminator except the first in the chainmeans are provided for inhibiting or correcting errors in theimmediately preceding discriminator.

Patented Dec. 28, 1971 3,631,469

5 Sheets-Sheet 1 FIG. I.

X F|G.4.

f I v v I g L L 3 L w L Y4 R 1 1 1 4 4 X16 16 64 Y64 264 v INVENTORRALPH LEVY AGENT Patented Dec. 28, 1971 5 Sheets-Sheet 5 Fig. IO

INVENTOR. RALPH LEVY AGEN Patented Dec. 28, .1971

5 Sheets-Sheet 4 Fig.

INVENTOR. RALPH LEVY AGE T Patented Dec. 28, 1971 3,631,469

5 Sheets-Sheet 5 RALPH LEVY BY jww/a ,6 AGEN'T SYSTEMS FOR COMPARINGELECTRICAL SIGNALS This invention relates to a system for comparing themagnitudes and the signs of two unidirectional electrical signals andfor indicating the result of such a comparison. This case is astreamline continuation of application Ser. No. 487,765 filed Sept. 16,I965 now abandoned.

The invention also relates to an electrical goniometric system arrangedto receive electrical signals proportional to sine and cosine functionsof an angle to be measured and to resolve and indicate the angle.

One manner of comparing two signals is to apply them respectively to twodeflection systems of a cathode-ray oscilloscope. Thus for instancesignal could be applied between the 1: terminals and the other betweenthe y terminals of the oscilloscope so as to add the two signals inquadrature; the angular attitude of the resultant linear trace appearingon the oscilloscope would then be determined by the relative magnitudesand signs of the two signals and the accuracy of such an oscilloscopedisplay can be improved by the addition of further displays arranged toprovide angular scale magnification of the original display. A similarmanner of resolving an angle from sine and cosine input signals is toapply them respectively to two deflection systems of a cathode-rayoscillator. Thus for instance one signal could be applied between the Xterminals and the other between the Y terminals of the oscilloscope; theangular attitude of the resultant linear trace appearing on theoscilloscope would then be determined by the relative magnitudes andsigns of the two signals. Such as angle may be considered as extendingfrom a datum line, for instance the positive y direction of aconventional Cartesian graph, and terminating in one of the fourquadrants of the graph; the termination of the angle, measured from thedatum line, is marked by the trace.

A disadvantage of a cathode-ray tube display system is that the displayis of a transient nature; an object of the present invention is toprovide an arrangement wherein if desired the in formation can beexpressed in a digital manner so that it can be indicated on a digitaldisplay device. Such a display, which may be arranged to continue longafter the information producing is has disappeared from the system, isnot of a transient nature as is the trace on a cathode-ray tube;further, information expressed in a digital manner can be recorded varyeasily and so preserved indefinitely.

The present invention, according to one aspect, provides a system forcomparing the amplitudes and signs of two simultaneous electricalsignals, wherein a chain of discriminators is arranged to determine withsuccessively greater resolution the angle P=tan X/Ywhere X and Yrespectively have the signs and amplitudes of each of the said twosignals, and wherein in each discriminator except the first in the chainmeans are provided for inhibiting or correcting errors in theimmediately preceding discriminator.

According to another aspect of the present invention an electricalgoniometric system comprises a chain of angle-measuring discriminatorsof successively greater resolution, wherein each discriminator isarranged to receive simultaneous electrical signals the magnitudes ofwhich are respectively proportional to the sine and cosine of an angleto be measured by the discriminator, wherein each discriminator isarranged to determine, relative to the datum, the quadrant of aCartesian representation in which the angle terminates, wherein eachdiscriminator except the first of the chain is arranged to operate withan expansion of four times the angular scale of the immediatelypreceding discriminator, and wherein each discriminator is arranged toproduce in binary digital form output signals indicative of the saidquadrant, whereby the angle P to be measured by the system can beindicated by the 1 output signals from all the discriminators in thechain. Each discriminator except the first of the chain may be arrangedto operate with an expansion of four timesthe angularscale of theimmediately preceding discriminator; each discriminator is provided witha logic circuit arranged to receive two input signals, to add the saidinput signals in space quadrature and to produce output indication inbinary form indicative of the quadrant of a Cartesian representation inwhich the resultant addition vector lies.

The invention is readily applicable, for example, to radiodirection-finding systems employing two or four aerials or aerialsystems arranged at right angles to each other. For example, with fouraerials two opposite aerials may produce between them a signal having anamplitude proportional to a sine function and two other opposite aerialswould then produce between them a signal having an amplitudeproportional to a cosine function; from these two signals theappropriate angle of the incident radio transmission relative to a fixeddirection can be determined.

Two embodiments of the invention will now be described with reference tothe accompanying diagrammatic drawings wherein:

FIG. 1 illustrates a cathode-ray tube display,

FIGS. 2 and 3 illustrate display patterns appropriate to the firstembodiment,

FIG. 4 is a block diagram of the system of the first embodiment,

FIG. 5 is a block diagram of a logic circuit for this system and FIG. 6illustrates the second embodiment,

FIG. 7 is a schematic diagram of the normalization circuits labeled withthe prefix S in FIG. 5.

FIG. 8, is a schematic diagram of the absolute magnitude stages labeledE in FIG. 5.

FIG. 9 is a schematic diagram of the difference stage labeled D in FIG.5.

7 FIG. 10 is a schematicdiagram of the comparator and sign splitterstages labeled C and H in FIG. 5.

FIG. 11 is .a schematic diagram of an alternative embodiment of thecomparator stage C.

FIG. 12 is a schematic diagram showing the interconnection of the E andDstages.

FIG. 13 is a schematic diagram of a portion of the scale expandercircuit labeled K in FIG. 5.

Consider two voltages at and y the magnitudes and polarities of which itis wished to compare. If these two voltages were applied to the X and Yterminals of a cathode-ray oscilloscope then a linear trace would beproduced as illustrated in FIG. I and would represent the vectorial sumof the two voltages when they are added in quadrature. The dispositionof this trace in one of the quadrants of the field of display, that isto say of the face of the cathode-ray tube, would indicate inconventional Cartesian form the signs, that is to say the polarities, ofthe quadrature components x and y; the angular displacement of the tracerelative to a datum position, here assumed to be the positive directionof the y axis, would bea function of the rel tive magnitudes of x and yand could be expressed by lX/yT -tan P (i) where x=sin P (ii) Now it canbe seen that the more accurately the angle P can be determined then themore accurately can the magnitudes of x and y be compared; if thereforewe provide an auxiliary cathode-ray tube which reproduces on an expandedangular scale the trace on the first tube then the ratio tan P can beaccurately determined.

In the presentisystem the input signal is applied to a chain ofdiscriminators having scale expansion of l, 4, l6...4" the final numberdepending on the degree of discrimination required.

Referring now to FIGS. 2, 3 and 4 of the drawings, FIG. 2 shows thepattern of a radial display of a 1 expansion discriminator, and FIG. 3shows a similar pattern for a 4 discriminator; the signals applied tothe chain of discriminators can conveniently be considered as derivedfrom the output terminals of an apparatus such as a direction-findingreceiver having sine and cosine outputs. The discriminators are arrangedso that as the l discriminator covers the range 0 to (quadrant 1,) the4' discriminator covers all four quadrants 1,, 2,, 3, and 4,, asindicated in the pattern of FIG. 2. Now if discriminator 1 has a slighterror so that a signal which should appear at 89 (quadrant 1,) actuallyappears at 91 (quadrant 2,), the signal will appear in quadrant 4,, at356 if the 4" discriminator is accurate. The system will record a signalin quadrants 2, and 4,, which represents an error of 90 in discriminatorI, that is one quarter of the total angular range, or if P isproportional to a frequency to be determined one quarter of the totalbandwidth.

In this embodiment the system eliminates this gross am- ;i7uity bynoting the signs of the difference between Y/ and on all discriminators.The gross ambiguities occur only in regions near the 90, 180 and 270positions, and in these regions Z #/Y/ --A\/ is unambiguously defined,as indicated in FIG. 2. Hence in the example quoted above, the correctindication of (/l/ is negative irrespective of whether the signal is at89 or 91 in the l, discriminator; it follows that the recorded result2,4, must be incorrect since it gives ,/-/x,/) as positive. The circuitlogic is arranged to change the result to 1,4,. The acceptable signs aresummarized in table I.

From this pattern and, indeed, from inspection of FIG. 2, it is clearthat provided the resultant signal lies within one of the regions(4.,+l,) near the 0, 90, 180 and 270 positions not more than one signwill require changing; this leads to the following rules:

1. If Y,is positive, then 2. X ,'Y,should equal Z,-X,; if it does not,then 3. If( /Y,/ x,/) is positive charge X, only,

and if (/Y,' /X,/ is negative change Y, only.

It is clear that as soon as the change of sign, if any, has beeneffected in a discriminator in the chain then the information giving thesign of Z may be ignored and only the signs of X and Y need be actuallyrecorded, except for the last discriminator which is not corrected byone four times more accurate. The signs of Z appear only within thesystem, having been determined solely in order to resolve theambiguities. The signchanging arrangements are described later withreference to FIG. 5.

As the system is based upon the principle of determining the value of Pwhen values of cos P and sin P, representing two components inquadrature, are given, then the solution obtained can be used toindicate either the value of the angle P or the value of the functiontan P, that is to say the ratio of the applied signals x=sin P and y=cosP.

Thus for example, suppose the angle P is to be determined to an accuracyof 1 part in 256 within the range 0 to 360 then only nine signs, that isnine binary digits, need be recorded; these nine binary digits comprisetwo quadrantlocating digits for each of four discriminators plus a digitindicating the sign of Z 2,, is equal to y/ /X/ for the lastdiscriminator.

Such a system is illustrated in block diagram form in FIG. 4 where the xand y signals are applied to a chain of discriminators each of whichcomprises a logic circuit L and each of which except the first alsocomprises a scale-expansion circuit K. The details of the scale expandercircuit K can be found in S. J. Robinson British Pat. No. 953,430 inparticular, FIG. 7 and page 5, line 45 to page 6, line 48.

The x and y signals applied to the input terminals of the logic circuitL of the first discriminator produce at the output terminals thereof abinary indication of the signs of x and y, which for convenience may bereferred to as X, and Y,. The x and y signals are also applied to thesecond discriminator of the chain, the output of the scale-expansioncircuit of each of the second and third discriminators being applied tothe next in the chain and also to the logic circuit L of thediscriminator. Now in each discriminator except the first thescale-expansion circuit is required to expand the angular scale of P sothat this angle can be determined more accurately: thus with inputs ofthe form x sin P and y cos P it must produce outputs x, sin 4P and y,cos 4P. Thus if for the purpose of illustration we put m1 then in FIG. 4we may write for the output of the 4 discriminator and input of the 16discriminator:

X, sin 4P Y, cos 4P and similarly for the output of the 16''discriminator and input of the 64 discriminator X sin l6P Y cos 16P andso on. In general, where n is the scale expansion factor,

Two binary digits appearat the output terminals of each of the fourlogic circuits L and an extra binary digit giving the sign of 2,,appears at an extra output terminal of the last logic circuit thusgiving a total of nine binary digits at the output terminals. Theseoutput terminals may feed indicators which indicate the signs of X,, Y,,...X,,,, Y,,,, 2,, as shown on FIG. 4. The x and Y indications fed backfrom next successive logic circuits will be described later withreference to FIG. 5. As the digits at the output terminals of the lastlogic circuit locate one of four possible divisions within thatdiscriminator then it follows that the angular resolution of the systemis I part in (64 4),that is 1 part in 256.

It should be borne in mind, when considering FIGS. 4 and 5, that the Xand Y outputs of each discriminator are in binary form: the magnitudesof the outputs at the recording terminals R, FIG. 5, are always the samebut the signs can change. The signals X,,, Y,, applied to the inputs ofthe discriminators can vary in both magnitude and sign.

In order to resolve uncertainties or to correct errors such for instanceas would occur when the tangent vector is near to the x or y axis theinformation of each discriminator is corrected with reference to thefour times greater accuracy of a 4' expanded discriminator. It isconceivable that all discriminators except the last one may requirecorrection, and the logic circuitry must be arranged so that thesuccessive changes may take place; some form of storage may be required,but this will be very short term storage, since all the information isimmediately available.

A block diagram of a circuit whichwill automatically perform the logicgiven by rules (1), (2) and (3) is shown in FIG. 5

The moduli of the signals X, and Y, are formed in stages E and are thensubtracted in a difierence stage D: the output of stage D isstandardized in voltage amplitude in a stage 82 so as to form Z,.

The signals X, and Y, appearing at the input terminals l are also eachstandardized in respective stages S, the signs only being retained, andthen pass through stages G which can be controlled to change or not tochange these signs as required. The output from the stages G is taken tooutput terminals R and also to a multiplying stage M at the output ofwhich appears the signal X ,'Y,.

A second multiplying stage M receives the Z, output and also an input X,from the logic circuit of the 4 discriminator and multiplies these twoto form X ,-Z,- The two products X ,-Y, and X,-Z, are compared in a signcomparator stage C and if these two products are not of the same sign,as required by rule (2), then the output from the stage C operates asignsplitter stage H and allows the output 2, from stage 52 to operatethe sign changer GX if Z, is positive or to operate the sign change GYif Z, is negative, so satisfying the requirements of rule (3). Thesign-splitter stage H includes a control gate which only allows thestage to operate if the Y1 signal applied to the stage is positive; thisgate is included so as to satisfy the requirements of rule (1). Thecorrected signals X, and Y, are then recorded.

All the circuit elements in FIG. 5 are simple switches, and hence havevery large dynamic range, except for the difference stage D. This isrequired only to decide whether /Y,/, or /X is the larger, and hence inthis stage, which preferably includes an amplifier, considerablecompression may be incorporated to achieve a large dynamic range.

The advantage of the system is accuracy to any desired power of 4, gooddynamic range and considerable simplicity, especially when compared withsystems previously proposed.

In the arrangement illustrated in FIG. 4 each of the 16 and 64discriminators derives its input from the preceding discriminator in thechain; with this arrangement each of the three 4, l6 and 64-discriminators expands the scale of its input signal by a factor of 4.In a modified form of this arrangement all the discriminators are fed inparallel from the X and Y terminals, the third discriminator is arrangedto have a scale expansion of 4 =l 6 and the fourth and lastdiscriminator is arranged to have a scale expansion of =64; in generaleach discriminator thus operates with a scale expansion of 4 where q isthe number of preceding discriminators in the chain.

A second embodiment again contains discriminators of expansion ratios 1,4, 16, etc. but the discriminators are staggered so that the 90 orcardinal points of discriminator 1 occur at the center, or 45 positionsof quadrant l of discriminator 4, as illustrated in the pattern diagramof FIG. 6. If it can be guaranteed that the nonlinearities in the twodiscriminators are such that quadrant 1, of discriminator 4 encloses thecardinal points, that is to say the x and y axis boundaries, ofdiscriminator l as illustrated by the shading in FIG. 6, then a grossquadrantal error in the digits from discriminator l is only possiblewhen the signal falls in quadrant 1,. Suppose that digits are set up torepresent the cardinal positions C1,, C2 C3, and C4,, and further thatthe digits representing C1, are the same as 1,, C2, the same as 2,, etc.It is clear that when the signal is at a frequency close to a cardinaldirection of discriminator I, then though the quadrant digits may be inerror there will be no errorin the cardinal-point digits. The appearanceof digits representing 1., may therefore be used to reject the quadrantdigits of discriminator 1 and accept the cardinal-point digits instead.For all other quadrants of discriminator 4, i.e., 2,, 3,, and 4,, thequadrant digits of discriminator 1 are selected. Thus the digitsrepresenting C l, or 1, indicate the quadrant AB of discriminator 1without possible error.

The quadrants are established by the signs of X and Y, and the cardinalpoints by the signs of (X-Y) and (/X//Y/'), as shown in table 11.

As indicated in table II, the condition in which the si 11 (X-Y) isnegative is used to reverse the sign of (/X/-/Y circuit techniquessimilar to those used in FIG. 5 being employed. The signs of X and Y maythen be used as the quadrant digits, and the signs of (x-Y) and (/X//Y/) as the cardinal-point digits. The condition that the digits, of 1,must be the same as those of Cl, and so on, is then fulfilled, becauseat the cardinal points th sign f X is the same as the sign of (X y) andthe sign of X/ K is the same as the sign of Y.

The accuracy of this second embodiment is similar to that of the firstembodiment, that is to say one quadrant of the final discriminator, buta higher degree of linearity is required from each discriminator inorder to achieve this accuracy. As it might be difficult to achieve thishigher degree of linearity in a practical discriminator the firstembodiment would probably be preferred; the advantage of the secondembodiment is that multiple sign corrections are avoided by thestaggering" of the discriminators.

FIG. 7 shows a circuit for standardizing (i.e., normalizing) an inputvoltage. Two diodes 100, 101 are reversed biased by the voltage sourcesor batteries 102, 103 respectively. Therefore, when the absolute valueof the input voltage exceeds a particular value, one of the diodes 102,103 will conduct and clip" the applied voltage, preventing the outputvoltage from exceeding this absolute value.

FIG. 8 shows the absolute magnitude indicator E which comprises fourdiodes 104, 105, 106, 107, arranged in a full wave bridge configuration.Thus, no matter what the polarity of the input voltage, the output willalways be of a selected polarity.

FIG. 9 shows the difference circuit D which comprises two decouplingresistors 108, 109 and a load resistor 110. Since the Y, input ispositive while the X, input is negative, the output be y X FIG. 10 showsthe comparator and sign splitter stages C and H. The comparator stagecomprises a full-wave rectifier 111, while the sign splitter stagefeatures a transistor 112 serving as a Y, input gate.

FIG. 11 shows an alternative embodiment of the comparator stagefeaturing a full-wave rectifier 113 and wherein the Y, gate 114 ispositioned within the comparator rather than in the signal splitterstage.

FIG. 12 shows the interconnection of absolute magnitude and differencestages. Note that the output polarities of the E stages are opposed inthe D stage so that the difference and not the sum is computed.

FIG. 13 shows the details of the scale expander circuit K of FIG. 4. Itcomprises sum and difference computers S1 S2, D1, D2; and square lawrectifiers 115, 116, and 117. The sum and difference computers can be asshown before or can be pulse transformers having two primaries and onesecondary. For the sum circuit the primary windings of each transformerare wound in the same direction; for the difference circuit in opposingdirections. The scale expander has two inputs X cos P and Y sin P. Sincethe square law rectifiers and the sum and difference computers performtheir named function, the voltages at various points in the circuit willbe as indicated because of the following trigonimetric identities:

2X Y= 2 cosP sinP= sin2P. Therefore, the output voltages of the circuitrepresent trigonimetric functions of twice the angle P. To get a voltagerepresenting four times the angle P, two of the above stages arecascaded.

Although, for convenience, the invention has been described inembodiments suitable for use with a directionfinding system, it will beunderstood that the invention is not limited to such an application butcan be readily adapted for any system where an angle is to be determinedfrom two signals one of which is proportional to the sine of the angleand the other of which is proportional to the cosine of the angle.

I claim:

1. A system for comparing the amplitude and polarities of twosimultaneous pulsed wide range direct current electrical signalsrepresenting the sine and cosine components of an angle to be measuredcomprising; first discriminator means for producing a first digitaloutput quantity having a value determined by the magnitude and polarityof said input signals and ALL indicating to a first approximation theangle to be measured, electrical scale expansion means coupled toreceive said input signals for producing angular scale expansion of theangle said signals represent, second discriminator means coupled to saidscale expansion means for producing a second digital output quantityindicating to a second approximation the angle to be measured; andcorrection means receiving continuously the entire second output forparallel correction of any errors in said first output whereby the angleto be measured is computed with greater accuracy.

2. A system as claimed in claim 1 wherein said scale expansion meansexpands the scale of said second discriminator to four times that ofsaid preceding first discriminator, whereby the output quantitiesrepresent successive Cartesian quadrants of the angle to be measured.

3. A system as claimed in claim 2 further comprising means for producingthe four quadrants of the output of the second discriminator whollywithin one quadrant of the first discriniinator.

4. A system as claim 2 further comprising means for producing theboundaries between adjacent quadrants in the first discriminator whollycontained within one particular quadrant of the second discriminatorwhereby the second discriminator generates output signals to indicatesaid boundaries.

n t w s

1. A system for comparing the amplitude and polarities of twosimultaneous pulsed wide range direct current electrical signalsrepresenting the sine and cosine components of an angle to be measuredcomprising; first discriminator means for producing a first digitaloutput quantity having a value determined by the magnitude and polarityof said input signals and indicating to a first approximation the angleto be measured, electrical scale expansion means coupled to receive saidinput signals for producing angular scale expansion of the angle saidsignals represent, second discriminator means coupled to said scaleexpansion means for producing a second digital output quantityindicating to a second approximation the angle to be measured; andcorrection means receiving continuously the entire second output forparallel correction of any errors in said first output whereby the angleto be measured is computed with greater accuracy.
 2. A system as claimedin claim 1 wherein said scale expansion means expands the scale of saidsecond discriminator to four times that of said preceding firstdiscriminator, whereby the output quantities represent successiveCartesian quadrants of the angle to be measured.
 3. A system as claimedin claim 2 further comprising means for producing the four quadrants ofthe output of the second discriminator wholly within one quadrant of thefirst discriminator.
 4. A system as claim 2 further comprising means forproducing the boundaries between adjacent quadrants in the firstdiscriminator wholly contained within one particular quadrant of thesecond discriminator whereby the second discriminator generates outputsignals to indicate said boundaries.